On How QCD Gauge Invariance Gets Realized in the Context of Effective Locality

H M Fried,T Grandou,R Hofmann

doi:10.1155/2018/2686507

Abstract

The fermionic Green’s functions of QCD exhibit an unexpected property of effective locality, which appears to be exact, involving no approximation. This property is nonperturbative, resulting from a full integration of the elementary gluonic degrees of freedom of QCD. Recalling, correcting, and extending the derivations of effective locality, focus is put on the way nonabelian gauge invariance gets realized in the fermionic nonperturbative regime of QCD.

Highlights

In some recent articles [1,2,3,4,5], a property, which bears on the nonperturbative fermionic Green’s functions of QCD, has been put forth under the name of effective locality (EL)
Recalling, correcting, and extending the derivations of effective locality, focus is put on the way nonabelian gauge invariance gets realized in the fermionic nonperturbative regime of QCD
It is worth pointing out that in the pure euclidean Yang Mills case and up to the first nontrivial orders of a semiclassical expansion, effective locality was observed as a welcome property in an attempt to construct a formulation dual to the original Yang Mills theory [6,7,8]

Summary

Introduction

In some recent articles [1,2,3,4,5], a property, which bears on the nonperturbative fermionic Green’s functions of QCD, has been put forth under the name of effective locality (EL). For any fermionic 2n-point Green’s functions and related amplitudes, the full gauge-fixed sum of cubic and quartic gluonic interactions, with fermionic loops included, results in a local contact-type interaction. EL functional expressions certainly attest to this difficulty It remains that, like in the pure Yang Mills situation of [6, 7], the EL property may allow one to learn something about the nonperturbative regime of QCD and this from first principles.

Contrasting Generating Functionals

Effective Locality in a Small Example

Effective Locality

Conclusion